Daniel is 30 years older than Umaima. Nine years ago, Daniel was 4 times as old as Umaima. How old is Umaima now?
Explanation: We can use the given information to write down two equations that describe the ages of Daniel and Umaima. Let Daniel's current age be $d$ and Umaima's current age be $u$ The information in the first sentence can be expressed in the following equation: $d = u + 30$ Nine years ago, Daniel was $d - 9$ years old, and Umaima was $u - 9$ years old. The information in the second sentence can be expressed in the following equation: $d - 9 = 4(u - 9)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $u$ , it might be easiest to use our first equation for $d$ and substitute it into our second equation. Our first equation is: $d = u + 30$ . Substituting this into our second equation, we get the equation: $(u + 30)$ $-$ $9 = 4(u - 9)$ which combines the information about $u$ from both of our original equations. Simplifying both sides of this equation, we get: $u + 21 = 4 u - 36$ Solving for $u$ , we get: $3 u = 57$ $u = 19$.